∫ e−e 1 ______________________________________ 16+e2x+ex(−8−2x)+8x+x2 log(x)+(2−x) log(x) (−128+e3x(2−x)−32x+24x2+10x3+x4+e2x(−24+6x+3x2)+ex(96−18x2−3x3)+(64x−e3xx+48x2+12x3+x4+e2x(12x+3x2)+ex(−48x−24x2−3x3)) log(x)+e 1 ______________________________________ 16+e2x+ex(−8−2x)+8x+x2 (64−e3x+48x+12x2+x3+e2x(12+3x)+ex(−48−24x−3x2)+(−2x+2exx) log(x))) ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________−64x+e3x x−48x2 −12x3 −x4 +e2x (−12x−3x2 )+ex (48x+24x2 +3x3 ) dx

3.9.59 $\int \frac {e^{-e^{\frac {1}{16+e^{2 x}+e^x (-8-2 x)+8 x+x^2}} \log (x)+(2-x) \log (x)} (-128+e^{3 x} (2-x)-32 x+24 x^2+10 x^3+x^4+e^{2 x} (-24+6 x+3 x^2)+e^x (96-18 x^2-3 x^3)+(64 x-e^{3 x} x+48 x^2+12 x^3+x^4+e^{2 x} (12 x+3 x^2)+e^x (-48 x-24 x^2-3 x^3)) \log (x)+e^{\frac {1}{16+e^{2 x}+e^x (-8-2 x)+8 x+x^2}} (64-e^{3 x}+48 x+12 x^2+x^3+e^{2 x} (12+3 x)+e^x (-48-24 x-3 x^2)+(-2 x+2 e^x x) \log (x)))}{-64 x+e^{3 x} x-48 x^2-12 x^3-x^4+e^{2 x} (-12 x-3 x^2)+e^x (48 x+24 x^2+3 x^3)} \, dx$

Optimal. Leaf size=21 \[ x^{2-e^{\frac {1}{\left (-4+e^x-x\right )^2}}-x} \]

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Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E^(-(E^(16 + E^(2*x) + E^x*(-8 - 2*x) + 8*x + x^2)^(-1)*Log[x]) + (2 - x)*Log[x])*(-128 + E^(3*x)*(2 - x)

- 32*x + 24*x^2 + 10*x^3 + x^4 + E^(2*x)*(-24 + 6*x + 3*x^2) + E^x*(96 - 18*x^2 - 3*x^3) + (64*x - E^(3*x)*x

+ 48*x^2 + 12*x^3 + x^4 + E^(2*x)*(12*x + 3*x^2) + E^x*(-48*x - 24*x^2 - 3*x^3))*Log[x] + E^(16 + E^(2*x) + E^

x*(-8 - 2*x) + 8*x + x^2)^(-1)*(64 - E^(3*x) + 48*x + 12*x^2 + x^3 + E^(2*x)*(12 + 3*x) + E^x*(-48 - 24*x - 3*

x^2) + (-2*x + 2*E^x*x)*Log[x])))/(-64*x + E^(3*x)*x - 48*x^2 - 12*x^3 - x^4 + E^(2*x)*(-12*x - 3*x^2) + E^x*(

48*x + 24*x^2 + 3*x^3)),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A] time = 1.29, size = 21, normalized size = 1.00 \begin {gather*} x^{2-e^{\frac {1}{\left (-4+e^x-x\right )^2}}-x} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^(-(E^(16 + E^(2*x) + E^x*(-8 - 2*x) + 8*x + x^2)^(-1)*Log[x]) + (2 - x)*Log[x])*(-128 + E^(3*x)*(

2 - x) - 32*x + 24*x^2 + 10*x^3 + x^4 + E^(2*x)*(-24 + 6*x + 3*x^2) + E^x*(96 - 18*x^2 - 3*x^3) + (64*x - E^(3

*x)*x + 48*x^2 + 12*x^3 + x^4 + E^(2*x)*(12*x + 3*x^2) + E^x*(-48*x - 24*x^2 - 3*x^3))*Log[x] + E^(16 + E^(2*x

) + E^x*(-8 - 2*x) + 8*x + x^2)^(-1)*(64 - E^(3*x) + 48*x + 12*x^2 + x^3 + E^(2*x)*(12 + 3*x) + E^x*(-48 - 24*

x - 3*x^2) + (-2*x + 2*E^x*x)*Log[x])))/(-64*x + E^(3*x)*x - 48*x^2 - 12*x^3 - x^4 + E^(2*x)*(-12*x - 3*x^2) +

E^x*(48*x + 24*x^2 + 3*x^3)),x]

[Out]

x^(2 - E^(-4 + E^x - x)^(-2) - x)

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fricas [A] time = 1.03, size = 35, normalized size = 1.67 \begin {gather*} e^{\left (-{\left (x - 2\right )} \log \relax (x) - e^{\left (\frac {1}{x^{2} - 2 \, {\left (x + 4\right )} e^{x} + 8 \, x + e^{\left (2 \, x\right )} + 16}\right )} \log \relax (x)\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*exp(x)*x-2*x)*log(x)-exp(x)^3+(3*x+12)*exp(x)^2+(-3*x^2-24*x-48)*exp(x)+x^3+12*x^2+48*x+64)*exp

(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(-x*exp(x)^3+(3*x^2+12*x)*exp(x)^2+(-3*x^3-24*x^2-48*x)*exp(x)+x^4+1

2*x^3+48*x^2+64*x)*log(x)+(2-x)*exp(x)^3+(3*x^2+6*x-24)*exp(x)^2+(-3*x^3-18*x^2+96)*exp(x)+x^4+10*x^3+24*x^2-3

2*x-128)*exp(-log(x)*exp(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(2-x)*log(x))/(x*exp(x)^3+(-3*x^2-12*x)*exp(

x)^2+(3*x^3+24*x^2+48*x)*exp(x)-x^4-12*x^3-48*x^2-64*x),x, algorithm="fricas")

[Out]

e^(-(x - 2)*log(x) - e^(1/(x^2 - 2*(x + 4)*e^x + 8*x + e^(2*x) + 16))*log(x))

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (x^{4} + 10 \, x^{3} + 24 \, x^{2} - {\left (x - 2\right )} e^{\left (3 \, x\right )} + 3 \, {\left (x^{2} + 2 \, x - 8\right )} e^{\left (2 \, x\right )} - 3 \, {\left (x^{3} + 6 \, x^{2} - 32\right )} e^{x} + {\left (x^{3} + 12 \, x^{2} + 3 \, {\left (x + 4\right )} e^{\left (2 \, x\right )} - 3 \, {\left (x^{2} + 8 \, x + 16\right )} e^{x} + 2 \, {\left (x e^{x} - x\right )} \log \relax (x) + 48 \, x - e^{\left (3 \, x\right )} + 64\right )} e^{\left (\frac {1}{x^{2} - 2 \, {\left (x + 4\right )} e^{x} + 8 \, x + e^{\left (2 \, x\right )} + 16}\right )} + {\left (x^{4} + 12 \, x^{3} + 48 \, x^{2} - x e^{\left (3 \, x\right )} + 3 \, {\left (x^{2} + 4 \, x\right )} e^{\left (2 \, x\right )} - 3 \, {\left (x^{3} + 8 \, x^{2} + 16 \, x\right )} e^{x} + 64 \, x\right )} \log \relax (x) - 32 \, x - 128\right )} e^{\left (-{\left (x - 2\right )} \log \relax (x) - e^{\left (\frac {1}{x^{2} - 2 \, {\left (x + 4\right )} e^{x} + 8 \, x + e^{\left (2 \, x\right )} + 16}\right )} \log \relax (x)\right )}}{x^{4} + 12 \, x^{3} + 48 \, x^{2} - x e^{\left (3 \, x\right )} + 3 \, {\left (x^{2} + 4 \, x\right )} e^{\left (2 \, x\right )} - 3 \, {\left (x^{3} + 8 \, x^{2} + 16 \, x\right )} e^{x} + 64 \, x}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*exp(x)*x-2*x)*log(x)-exp(x)^3+(3*x+12)*exp(x)^2+(-3*x^2-24*x-48)*exp(x)+x^3+12*x^2+48*x+64)*exp

(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(-x*exp(x)^3+(3*x^2+12*x)*exp(x)^2+(-3*x^3-24*x^2-48*x)*exp(x)+x^4+1

2*x^3+48*x^2+64*x)*log(x)+(2-x)*exp(x)^3+(3*x^2+6*x-24)*exp(x)^2+(-3*x^3-18*x^2+96)*exp(x)+x^4+10*x^3+24*x^2-3

2*x-128)*exp(-log(x)*exp(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(2-x)*log(x))/(x*exp(x)^3+(-3*x^2-12*x)*exp(

x)^2+(3*x^3+24*x^2+48*x)*exp(x)-x^4-12*x^3-48*x^2-64*x),x, algorithm="giac")

[Out]

integrate(-(x^4 + 10*x^3 + 24*x^2 - (x - 2)*e^(3*x) + 3*(x^2 + 2*x - 8)*e^(2*x) - 3*(x^3 + 6*x^2 - 32)*e^x + (

x^3 + 12*x^2 + 3*(x + 4)*e^(2*x) - 3*(x^2 + 8*x + 16)*e^x + 2*(x*e^x - x)*log(x) + 48*x - e^(3*x) + 64)*e^(1/(

x^2 - 2*(x + 4)*e^x + 8*x + e^(2*x) + 16)) + (x^4 + 12*x^3 + 48*x^2 - x*e^(3*x) + 3*(x^2 + 4*x)*e^(2*x) - 3*(x

^3 + 8*x^2 + 16*x)*e^x + 64*x)*log(x) - 32*x - 128)*e^(-(x - 2)*log(x) - e^(1/(x^2 - 2*(x + 4)*e^x + 8*x + e^(

2*x) + 16))*log(x))/(x^4 + 12*x^3 + 48*x^2 - x*e^(3*x) + 3*(x^2 + 4*x)*e^(2*x) - 3*(x^3 + 8*x^2 + 16*x)*e^x +

64*x), x)

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maple [A] time = 0.08, size = 43, normalized size = 2.05


method	result	size

risch	$x^{-{\mathrm e}^{-\frac {1}{2 \,{\mathrm e}^{x} x -x^{2}-{\mathrm e}^{2 x}+8 \,{\mathrm e}^{x}-8 x -16}}} x^{2-x}$	$43$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((2*exp(x)*x-2*x)*ln(x)-exp(x)^3+(3*x+12)*exp(x)^2+(-3*x^2-24*x-48)*exp(x)+x^3+12*x^2+48*x+64)*exp(1/(exp

(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(-x*exp(x)^3+(3*x^2+12*x)*exp(x)^2+(-3*x^3-24*x^2-48*x)*exp(x)+x^4+12*x^3+4

8*x^2+64*x)*ln(x)+(2-x)*exp(x)^3+(3*x^2+6*x-24)*exp(x)^2+(-3*x^3-18*x^2+96)*exp(x)+x^4+10*x^3+24*x^2-32*x-128)

*exp(-ln(x)*exp(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(2-x)*ln(x))/(x*exp(x)^3+(-3*x^2-12*x)*exp(x)^2+(3*x^

3+24*x^2+48*x)*exp(x)-x^4-12*x^3-48*x^2-64*x),x,method=_RETURNVERBOSE)

[Out]

x^(-exp(-1/(2*exp(x)*x-x^2-exp(2*x)+8*exp(x)-8*x-16)))*x^(2-x)

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maxima [A] time = 0.96, size = 37, normalized size = 1.76 \begin {gather*} x^{2} e^{\left (-x \log \relax (x) - e^{\left (\frac {1}{x^{2} - 2 \, {\left (x + 4\right )} e^{x} + 8 \, x + e^{\left (2 \, x\right )} + 16}\right )} \log \relax (x)\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*exp(x)*x-2*x)*log(x)-exp(x)^3+(3*x+12)*exp(x)^2+(-3*x^2-24*x-48)*exp(x)+x^3+12*x^2+48*x+64)*exp

(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(-x*exp(x)^3+(3*x^2+12*x)*exp(x)^2+(-3*x^3-24*x^2-48*x)*exp(x)+x^4+1

2*x^3+48*x^2+64*x)*log(x)+(2-x)*exp(x)^3+(3*x^2+6*x-24)*exp(x)^2+(-3*x^3-18*x^2+96)*exp(x)+x^4+10*x^3+24*x^2-3

2*x-128)*exp(-log(x)*exp(1/(exp(x)^2+(-2*x-8)*exp(x)+x^2+8*x+16))+(2-x)*log(x))/(x*exp(x)^3+(-3*x^2-12*x)*exp(

x)^2+(3*x^3+24*x^2+48*x)*exp(x)-x^4-12*x^3-48*x^2-64*x),x, algorithm="maxima")

[Out]

x^2*e^(-x*log(x) - e^(1/(x^2 - 2*(x + 4)*e^x + 8*x + e^(2*x) + 16))*log(x))

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mupad [B] time = 1.26, size = 37, normalized size = 1.76 \begin {gather*} \frac {x^2}{x^{{\mathrm {e}}^{\frac {1}{8\,x+{\mathrm {e}}^{2\,x}-8\,{\mathrm {e}}^x-2\,x\,{\mathrm {e}}^x+x^2+16}}}\,x^x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(- log(x)*(x - 2) - exp(1/(8*x + exp(2*x) - exp(x)*(2*x + 8) + x^2 + 16))*log(x))*(exp(2*x)*(6*x + 3*

x^2 - 24) - 32*x - exp(x)*(18*x^2 + 3*x^3 - 96) + exp(1/(8*x + exp(2*x) - exp(x)*(2*x + 8) + x^2 + 16))*(48*x

- exp(3*x) - log(x)*(2*x - 2*x*exp(x)) - exp(x)*(24*x + 3*x^2 + 48) + exp(2*x)*(3*x + 12) + 12*x^2 + x^3 + 64)

- exp(3*x)*(x - 2) + log(x)*(64*x + exp(2*x)*(12*x + 3*x^2) - x*exp(3*x) + 48*x^2 + 12*x^3 + x^4 - exp(x)*(48

*x + 24*x^2 + 3*x^3)) + 24*x^2 + 10*x^3 + x^4 - 128))/(64*x + exp(2*x)*(12*x + 3*x^2) - x*exp(3*x) + 48*x^2 +

12*x^3 + x^4 - exp(x)*(48*x + 24*x^2 + 3*x^3)),x)

[Out]

x^2/(x^exp(1/(8*x + exp(2*x) - 8*exp(x) - 2*x*exp(x) + x^2 + 16))*x^x)

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sympy [A] time = 150.73, size = 37, normalized size = 1.76 \begin {gather*} e^{\left (2 - x\right ) \log {\relax (x )} - e^{\frac {1}{x^{2} + 8 x + \left (- 2 x - 8\right ) e^{x} + e^{2 x} + 16}} \log {\relax (x )}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*exp(x)*x-2*x)*ln(x)-exp(x)**3+(3*x+12)*exp(x)**2+(-3*x**2-24*x-48)*exp(x)+x**3+12*x**2+48*x+64)

*exp(1/(exp(x)**2+(-2*x-8)*exp(x)+x**2+8*x+16))+(-x*exp(x)**3+(3*x**2+12*x)*exp(x)**2+(-3*x**3-24*x**2-48*x)*e

xp(x)+x**4+12*x**3+48*x**2+64*x)*ln(x)+(2-x)*exp(x)**3+(3*x**2+6*x-24)*exp(x)**2+(-3*x**3-18*x**2+96)*exp(x)+x

**4+10*x**3+24*x**2-32*x-128)*exp(-ln(x)*exp(1/(exp(x)**2+(-2*x-8)*exp(x)+x**2+8*x+16))+(2-x)*ln(x))/(x*exp(x)

**3+(-3*x**2-12*x)*exp(x)**2+(3*x**3+24*x**2+48*x)*exp(x)-x**4-12*x**3-48*x**2-64*x),x)

[Out]

exp((2 - x)*log(x) - exp(1/(x**2 + 8*x + (-2*x - 8)*exp(x) + exp(2*x) + 16))*log(x))

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